A k-signed r-set on [n] = {1, ..., n} is an ordered pair (A, f), where A is an rsubset of [n] and f is a function from A to [k]. Families A1, ..., Ap are said to be cross-intersec...
The Helly number of a family of sets with empty intersection is the size of its largest inclusionwise minimal sub-family with empty intersection. Let F be a finite family of open...
Given a set of points in the plane, a crossing family is a collection of line segments, each joining two of the points, such that any two line segments intersect internally. Two s...
We introduce the notion of an unrefinable decomposition of a 1-design with at most two block intersection numbers, which is a certain decomposition of the 1-designs collection of ...
In this paper, we attempt a systematic study of QL-implications. Towards this end, firstly, we investigate the conditions under which a QL-operation becomes a fuzzy implication w...